Analytical Solutions of a One-Dimensional Linear Model Describing Scale Inhibitor Precipitation Treatments

Abstract

The deposition of mineral scales such as barium sulfate and calcium carbonate in producing oil wells is a well-known problem in the oil industry, costing many millions of dollars per year to solve. The main preventative measure for managing downhole scale is to inject chemical scale inhibitor (SI) back into the producing well and out into the near well reservoir formation in a so-called "squeeze" treatment. The scale inhibitor is retained in and subsequently released from the formation by the two main mechanisms of "adsorption" ( ) and "precipitation" ( ). As the well is brought back onto production, the scale inhibitor then desorbs (adsorption) or re-dissolves (precipitation) and the low SI concentration that is present in the produced water effectively retards the scale deposition process. A complete model of SI retention must have a full kinetic / model embedded in a transport model for flow through porous media. In this paper, we present a subcase of this model involving only kinetic precipitation ( ). The simple quasi-linear problem with an infinite source of precipitate is straightforwardly soluble using conventional methods for a precipitate described by a solubility C s and a dissolution rate κ. However, the problem with a finite amount of precipitate is more complex and novel analytical solutions are presented for the (transient) behavior for this case. The mathematical difficulty in this latter system arises because, when the precipitate is fully dissolved close to the system inlet, a moving internal boundary develops along with some related flow regions defined by the parameters of the problem. The problem is solved here by making certain assumptions about the internal moving point at position α , where = 0, and we derive an expression for the velocity of this point (dα /dt). From this, we then build the solution for all possible regions which may develop (depending on the problem parameters). Understanding the behavior of this idealized system gives us some practical formulae for precipitation squeeze design purposes. It also serves as an important

Preparation and Laboratory Testing of Polymeric Scale Inhibitor Colloidal Materials for Oilfield Mineral Scale Control

“…The flow back of the synthetic brine in LSSE is to mimic the flow of production fluid out of the reservoir formation. During this process, the production fluid would be in contact with the retained inhibitor and gradually release the retained inhibitor back into aqueous production fluid for the scale control (an inhibitor return process) [ 13 , 14 , 15 , 16 ]. An inhibitor return curve can be established by plotting the effluent inhibitor concentration versus the number of PVs of the brine returned during an LSSE.…”

“…With the progression of inhibitor return, the aqueous concentration of inhibitor in the production fluid (return concentration) will progressively decline over time. When the return concentration is low enough, another squeeze treatment might be necessitated to elevate the inhibitor return concentration to effectively control scale threats [ 15 ]. The time duration between two consecutive squeeze treatments is called the squeeze lifetime.…”

Analytical Solutions for a 1D Scale Inhibitor Transport Model with Coupled Adsorption and Precipitation

“…3 and contrasted with the "pure dissolution" (i.e. Γ 0 = 0 ) solution obtained in a previous paper (Sorbie and Stamatiou 2018). Equilibrium desorption causes a retardation of concentration values with respect to the "water front" moving through the system at velocity v. In the region V L C s t ≤ x ≤ vt , a bank of C = C s is sustained.…”

“…(5) to change its form to C∕ t + V L (C) C∕ x = 0 . Analogous to the argument given in Sorbie and Stamatiou (2018), it will be convenient to introduce also the point C = C (t) such that C ≡ 0 for x ≤ C and C > 0 for x > C . Since C ≡ 0 is not a solution of Eq.…”